In my experience, I'd say the necks on the 60s CV precisions are among the thinner/smaller P bass necks you'll find. I've played some absolute bloody logs in the name of P bass necks in the past, both Fender and copies.
Might be an idea to whip the neck off a precision and replace with a Jazz one if that is uncomfortable for you. I doubt you;ll get anything noticeably more manageable.
Or another idea could be to buy a PBass and re shape the neck to whatever contour you like. Won't help with the width but might make it more comfortable. I really don't know why neck re shaping isn't more common in guitar/bass circles. It's a piece of piss to do.